Beyond the effectiveness of machine learning methods, a second aspect should be ensured: the interpretability of the decision-making process, as well as the explanation of the results. For safety-critical domains, as mental health is, it is mandatory that Artificial Intelligence (AI) systems be transparent and trustworthy to both practitioners and patients. This paper presents a systematic review revealing how interpretability, explainability, and ethic are considered in AI techniques for healthcare. We evaluate the effectiveness of machine learning models in the particular case of detecting stress. We consider methods with different support for interpretability like logistic regression (inherently interpretable), SS3 (adequate interpretability) and BERT/MentalBERT (black-boxes). The results of the experimental study show that logistic regression and SS3 have slightly lower predictive performance than transformer-based models, which are complex and difficult to explain. From the interpretable models, we can confirm the conclusions presented in previous works about the role that personal pronouns and self-references play as significant indicators of stress. This was possible due to the ability of logistic regression to assess the individual importance of each input token and the ability of SS3 to hierarchically classify and interpret input words/sentences/paragraphs. On the other hand, the same conclusion was derived from attention analysis performed for the Transformer-based methods despite their inherent opacity.